Question

A catalyst adsorbs $100$ mL of nitrogen gas at S.T.P. per gram of catalyst surface and forms as a mono-molecular layer. The effective surface area occupied by one nitrogen molecule on the surface of catalyst is $0.16\times {10}^{–14}{\text{cm}}^2$ . What is the total surface area occupied by nitrogen molecules per gram of catalyst?
(Given: Volume of gas at STP = 22.4 L)

• A. $43.04\times {10}^5{\text{cm}}^2$
• B. $0.18\times {10}^{–15}{\text{cm}}^2$
• C. $42\times {10}^5{\text{cm}}^2$
• D. $0.19\times 9^{–15}{\text{cm}}^2$

Answer 1

The correct option is A $43.04\times {10}^5{\text{cm}}^2$

Number of nitrogen molecules $\left(N\right)$ $=\frac{\text{volume (mL)}\times N_A}{\text{volume of STP (in mL)}}$
$\Rightarrow N=\frac{100}{22400}\times 6.023\times {10}^{23}=2.69\times {10}^{21}$
Surface area occupied by one molecule $=0.16\times {10}^{–14}{\text{cm}}^2$
Total area covered by $N_2$(g)/gram of catalyst $=0.16\times {10}^{–14}\times 2.69\times {10}^{21}=43.04\times {10}^5{\text{cm}}^2$